Fig. 4: Breakdown of power-law behavior.

The plots show empirical exceedance probabilities on a semi-logarithmic scale; the samples are the same as shown in Fig. 2, with (a) thermal, and (b) BSV pumping. The same values for the power-law interval [m, M] are indicated by vertical lines. The dark blue solid lines show exponential fits, to observations above 5 ⋅ 10⁴ in the thermal case, and between 2 ⋅ 10⁵ and M^* = 10⁶ in the BSV case, providing exponential rate parameter estimates of \({\hat{\lambda }}_{a}=2.6\cdot 1{0}^{-5}\) and \({\hat{\lambda }}_{b}=1.9\cdot 1{0}^{-6}\), respectively. The brown dashed line shows the generalized Pareto fit of the observations beyond M^*, with \({\hat{i}}_{\max }=1.58\cdot 1{0}^{6}\) and \(\hat{\gamma }=1.59\).